Most newspapers and other news sources have Twitter feeds. You get the headlines, often with links to longer articles. You don't need a Twitter account to access them but it helps as you can then follow the ones of interest to you, which means you automatically see tweets as they are posted instead of having to check each source in turn manually. Provided you choose appropriate sources to follow you'll never encounter any celeb publicity garbage or nonsense trivia posted by private individuals. Nor would you ever need to post any tweets yourself unless you want to.